The aim of the present r e s earch was to find an ac curat e pred i c t i on e quati on that can be used i n food fre e z er d e s i gn . De s irable criteri a for a sui table s oluti on are :
1 . Suffi c i ent ac curacy for engine ering purp o ses .
2 . Appli cabil i ty t o a wid e range o f si z e s , shapes and fo od material s .
3 . Simpl i city .
4 . Appl i cabili ty t o the common pract i c al s i tuati on o f th e third k ind o f bound ary c onditi on .
5 . Appli cabi li ty to probl em s where the m at eri al i s initial ly superh eated above i t s fre e z ing point .
6 . I•!inimal need for thermal pro perty d at a .
The n e ed for the sixth criterion ari s e s fro n the fac t that the r e i s a l ack of d e t ai l ed m ea suremen t s o f therm al propert i e s of fo od s . C o mmonly , only a few value s at d i ffer ent t e mperature s and water c ontent s are kn own for any fo od s tuff. Hence it is cl early an advant age if the d e sign
e quat i on d o e s n o t require d etailed informat i on on the thermal propert ie s .
Analyt i c al s o luti on o f fre e z ing problem s with th e third kind o f b oundary condition and in i t i al superheat i s very d ifficul t be caus e of the non-linear b oundary c ond i t i on s ,
but th ere are a number o f approxim ati ons t o the s o lut i o n s o f pro bl em s o f thi s type . I t was d e c ided t o e x�1ine , crit i cally , avail able solution s to s e e i f any are s uffi c i ently ac curat e , wi th or without m odifi c at ion , for d e s ign purpo s e s . Only r egular ge om etric shap e s were consid ered in d etail
be caus e limi tat i on s on tim e preven t e d a ful l s urvey b e in g m ad e . The s t e p s involved in the investigat i on were as fol l o ws :
1 . C o ll e cti on of accurate experimental d ata for fre e zing of foo d materi al s over a w i d e range o f c ondit i ons wi th four d i fferent shap e s - slab s , cylind ers , sphere s and r e ctangular bri ck s .
2 . For each shape , inve stigati on of avail abl e s ol u t i o n s t o s e e whi ch , i f an y, give ac curate predicti on o f fre e z ing t ime ove r a range o f conditi ons when compare d t o the exp erim en t ally measured fre e z in g tim e s . The s e s oluti ons were divided into two group s .
(
i)
Tho s e requiring a computer for c al culat i on of the fre ezing tim e . Thi s group in c lud e s s olut ions re quiring num eri cal integration , and fin i t e di fferenc e and fin ite e lement soluti on s .(
i i)
Th o s e ·suffi c i entl y simple t o allow hand cal cul at i on , hereafter referred to as 11simpl eformul ae " . Thi s group m ainly compri s e s the approx imate an alyti c al s oluti ons and the em piri cally modi fi ed formulae .
The d ivi s i on o f the soluti ons into two cat e gori e s was based o n rel ative s i mpl i c ity . I'·lany engi n e er s i n a p o s i t i on where they must pred ict a fo o d fre e z ing time d o not have ac c e s s to a computer and must th erefore rely on simpl e formulae . On the o th er hand , a per s on wi th a c om puter avail abl e wil l u s e a c omputer-based s o luti on i f i t i s more ac curate
than a s impl e formul a .
3 . The b e st s o luti ons i n e ach o f the two categori e s for the various shape s were considered t o s e e whi ch i s the superi or m ethod for predicting the fre e z ing
tim e s o f food m aterial s .
4 . Finally , al though it was n o t p o s s ible t o s tudy irre gular shape s in d e t ai l , the trend s found in the inve s t i gati on of fre e zing time cal culati on s for regular shapes were appli ed t o irregul ar shap e s on a the oreti c al bas i s . The resul t s o f thi s should provide a guidel ine t o the d e s i gn engineer attempting to pred i c t the free zing tim e of an i rregularly-shaped package o f fo od .
4 COLLECTI ON OF EXPERH1ENTAL DATA